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Outcome-Based Branch and Bound Algorithm for Optimization over the Efficient Set and Its Application

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Some Current Advanced Researches on Information and Computer Science in Vietnam (NAFOSTED 2014)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 341))

Abstract

The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. Because of its interesting mathematical aspects as well as its wide range of applications, this problem has attracted the attention of many authors. In this article, we propose a branch and bound algorithm in outcome space for minimizing a function \(h(x)=\varphi (f(x))\) over the efficient set \(X_{E}\) of the bi-criteria convex programming problem \(\mathrm{{Vmin}}\{f(x)=(f_{1}(x),f_{2}(x))^{T}|x\in X\}\), where the function \(\varphi \) is a quasi-concave function defined on \(f(X)\). The convergence of the algorithm is established. Preliminary computational results are reported.

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number “101.01-2013.19”.

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Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

    Tran Ngoc Thang

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  1. Tran Ngoc Thang
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Correspondence to Tran Ngoc Thang .

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Editors and Affiliations

  1. Institute of Information Technology, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Quang A. Dang

  2. IT Research and Development Center, Hanoi University, Hanoi, Vietnam

    Xuan Hoai Nguyen

  3. Faculty of Information Technology, University of Science, Hochiminh, Vietnam

    Hoai Bac Le

  4. University of Engineering and Technology, Hanoi, Vietnam

    Viet Ha Nguyen

  5. Posts and Telecommunications Institute of Technology, Ho Chi Minh, Vietnam

    Vo Nguyen Quoc Bao

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Thang, T.N. (2015). Outcome-Based Branch and Bound Algorithm for Optimization over the Efficient Set and Its Application. In: Dang, Q., Nguyen, X., Le, H., Nguyen, V., Bao, V. (eds) Some Current Advanced Researches on Information and Computer Science in Vietnam. NAFOSTED 2014. Advances in Intelligent Systems and Computing, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-319-14633-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-14633-1_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14632-4

  • Online ISBN: 978-3-319-14633-1

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